The total pressure on the top of a closed cylindrical vessel completely filled up with a liquid is

Answer: Option C

The total pressure on the top of a closed cylindrical vessel completely filled with a liquid is directly proportional to (radius)⁴. This phenomenon is a result of the distribution of pressure in a fluid due to its weight.
When a vessel is completely filled with liquid, the pressure at a specific depth is determined by the weight of the liquid above that level. The pressure at any point within a static fluid is proportional to the height of the fluid column above that point. For a cylindrical vessel, the pressure distribution is influenced by the cross-sectional area, which is proportional to the square of the radius.
Since the pressure is directly related to the height of the liquid column and the area of the cross-section (which is proportional to the radius squared), the total pressure on the top of the vessel will be directly proportional to (radius)² * (radius)², which simplifies to (radius)⁴.